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A still sharper region where p(x) - li(x) is positive**

Saputer, Yannick; Trudgian, Timothy; Demichel, Patrick


We consider the least number x for which a change of sign of π(x) − li(x) occurs. First, we consider modifications of Lehman’s method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
Source: Mathematics of Computation
DOI: 10.1090/S0025-5718-2015-02930-5


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